The East Dunbartonshire MP, who was a minister in the previous coalition government, is understood to have been reported by one of her constituents.
Police Scotland have received an initial complaint and the force is looking into the circumstances.
It comes after Ms Swinson took back the seat she had lost to the SNP in June's snap General Election.
The East Dunbartonshire constituency was one of the Liberal Democrats' top targets in Scotland after Ms Swinson represented the area between 2005 and 2015. Her election expenses were reported to be just £210 below the legal limit, after £7,000 worth of costs were disregarded as going towards election materials that weren't delivered, or national spending.
In August, the SNP claimed Ms Swinson was "living dangerously close to spending limits" and faced "serious questions".
A spokesman for the Liberal Democrats said: "All expenditure in this election was apportioned correctly and clearly identified in our election return which is a matter of public record."
Police Scotland last year investigated claims regarding Lib Dem MSP Alex Cole-Hamilton's expenses from the 2016 Holyrood election, with the Crown Office confirming later that he would not be prosecuted.
The Liberal Democrat spokesman claimed the complaint was a "classic SNP tactic when they have lost an election".
The spokesman said: "Last year they wasted 13 months of police time with their complaint about the election in Edinburgh Western, and the police found there was no case to answer.
"As in Edinburgh Western, we have full confidence that there is no substance to this complaint.
"We make no apology for fighting as hard as we could to stop the SNP in their tracks. The people of East Dunbartonshire made a clear choice when they rejected the SNP in June.
“With Police Scotland in turmoil as a result of the SNP’s botched reforms, the police have got enough to deal with. SNP boss Peter Murrell should bring to an end this nonsense of making unfounded complaints to the police whenever the SNP are sore about losing an election.”